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## Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions

Fonte: Public Library of Science
Publicador: Public Library of Science

Tipo: Artigo de Revista Científica

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Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally...

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## Rhesus Monkeys (Macaca mulatta) Spontaneously Compute Addition Operations Over Large Numbers

Fonte: Elsevier
Publicador: Elsevier

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Mathematics is a uniquely human capacity. Studies of animals and human infants reveal, however, that this capacity builds on language-independent mechanisms for quantifying small numbers (< 4) precisely and large numbers approximately. It is unclear whether animals and human infants can spontaneously tap mechanisms for quantifying large numbers to compute mathematical operations. Moreover, all available work on addition operations in non-human animals has confounded number with continuous perceptual properties (e.g. volume, contour length) that correlate with number. This study shows that rhesus monkeys spontaneously compute addition operations over large numbers, as opposed to continuous extents, and that the limit on this ability is set by the ratio difference between two numbers as opposed to their absolute difference.; Psychology

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## Joint Compute and Forward for the Two Way Relay Channel with Spatially Coupled LDPC Codes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/05/2012
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We consider the design and analysis of coding schemes for the binary input
two way relay channel with erasure noise. We are particularly interested in
reliable physical layer network coding in which the relay performs perfect
error correction prior to forwarding messages. The best known achievable rates
for this problem can be achieved through either decode and forward or compute
and forward relaying. We consider a decoding paradigm called joint compute and
forward which we numerically show can achieve the best of these rates with a
single encoder and decoder. This is accomplished by deriving the exact
performance of a message passing decoder based on joint compute and forward for
spatially coupled LDPC ensembles.; Comment: This paper was submitted to IEEE Global Communications Conference
2012

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## The Degrees of Freedom of Compute-and-Forward

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We analyze the asymptotic behavior of compute-and-forward relay networks in
the regime of high signal-to-noise ratios. We consider a section of such a
network consisting of K transmitters and K relays. The aim of the relays is to
reliably decode an invertible function of the messages sent by the
transmitters. An upper bound on the capacity of this system can be obtained by
allowing full cooperation among the transmitters and among the relays,
transforming the network into a K times K multiple-input multiple-output (MIMO)
channel. The number of degrees of freedom of compute-and-forward is hence at
most K. In this paper, we analyze the degrees of freedom achieved by the
lattice coding implementation of compute-and-forward proposed recently by Nazer
and Gastpar. We show that this lattice implementation achieves at most
2/(1+1/K)\leq 2 degrees of freedom, thus exhibiting a very different asymptotic
behavior than the MIMO upper bound. This raises the question if this gap of the
lattice implementation to the MIMO upper bound is inherent to
compute-and-forward in general. We answer this question in the negative by
proposing a novel compute-and-forward implementation achieving K degrees of
freedom.; Comment: 32 pages, to appear in IEEE Transactions on Information Theory

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## Decode-forward and Compute-forward Coding Schemes for the Two-Way Relay Channel

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/08/2011
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We consider the full-duplex two-way relay channel with direct link between
two users and propose two coding schemes: a partial decode-forward scheme, and
a combined decode-forward and compute-forward scheme. Both schemes use
rate-splitting and superposition coding at each user and generate codewords for
each node independently. When applied to the Gaussian channel, partial
decode-forward can strictly increase the rate region over decode-forward, which
is opposite to the one-way relay channel. The combined scheme uses
superposition coding of both Gaussian and lattice codes to allow the relay to
decode the Gaussian parts and compute the lattice parts. This scheme can also
achieve new rates and outperform both decode-forward and compute-forward
separately. These schemes are steps towards understanding the optimal coding.; Comment: To appear in Information Theory Workshop (ITW) 2011

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## How to compute Green's Functions for entire Mass Trajectories within Krylov Solvers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The availability of efficient Krylov subspace solvers play a vital role for
the solution of a variety of numerical problems in computational science. Here
we consider lattice field theory. We present a new general numerical method to
compute many Green's functions for complex non-singular matrices within one
iteration process. Our procedure applies to matrices of structure $A=D-m$, with
$m$ proportional to the unit matrix, and can be integrated within any Krylov
subspace solver. We can compute the derivatives $x^{(n)}$ of the solution
vector $x$ with respect to the parameter $m$ and construct the Taylor expansion
of $x$ around $m$. We demonstrate the advantages of our method using a minimal
residual solver. Here the procedure requires $1$ intermediate vector for each
Green's function to compute. As real life example, we determine a mass
trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we
can obtain Green's functions at all masses $\geq m$ at the price of one
inversion at mass $m$.; Comment: 11 pages, 2 eps-figures, needs epsf.sty

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## How to Compute Worst-Case Execution Time by Optimization Modulo Theory and a Clever Encoding of Program Semantics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/05/2014
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In systems with hard real-time constraints, it is necessary to compute upper
bounds on the worst-case execution time (WCET) of programs; the closer the
bound to the real WCET, the better. This is especially the case of synchronous
reactive control loops with a fixed clock; the WCET of the loop body must not
exceed the clock period. We compute the WCET (or at least a close upper bound
thereof) as the solution of an optimization modulo theory problem that takes
into account the semantics of the program, in contrast to other methods that
compute the longest path whether or not it is feasible according to these
semantics. Optimization modulo theory extends satisfiability modulo theory
(SMT) to maximization problems. Immediate encodings of WCET problems into SMT
yield formulas intractable for all current production-grade solvers; this is
inherent to the DPLL(T) approach to SMT implemented in these solvers. By
conjoining some appropriate "cuts" to these formulas, we considerably reduce
the computation time of the SMT-solver. We experimented our approach on a
variety of control programs, using the OTAWA analyzer both as baseline and as
underlying microarchitectural analysis for our analysis, and show notable
improvement on the WCET bound on a variety of benchmarks and control programs.; Comment: ACM SIGPLAN/SIGBED Conference on Languages...

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## Technical Note: Radiotherapy dose calculations using GEANT4 and the Amazon Elastic Compute Cloud

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/05/2011
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Cloud computing allows for vast computational resources to be leveraged
quickly and easily in bursts as and when required. Using the Amazon Elastic
Compute Cloud and the Amazon Simple Storage Solution, we describe a technique
that allows for Monte Carlo radiotherapy dose calculations to be performed
using GEANT4 and executed in the cloud. Simulation cost and completion time was
evaluated as a function of instance count using compute instances acquired via
biding on the Elastic Compute Cloud spot market. Bidding for instances on the
instance spot market was found to be 35-60% of the cost of on-demand instances
of the same type. Using the technique, we demonstrate the potential usefulness
of cloud computing as a solution for rapid Monte Carlo simulation for
radiotherapy dose calculation.

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## How to Compute Times of Random Walks based Distributed Algorithms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/07/2008
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#Computer Science - Distributed, Parallel, and Cluster Computing#Computer Science - Discrete Mathematics

Random walk based distributed algorithms make use of a token that circulates
in the system according to a random walk scheme to achieve their goal. To study
their efficiency and compare it to one of the deterministic solutions, one is
led to compute certain quantities, namely the hitting times and the cover time.
Until now, only bounds on these quantities were defined. First, this paper
presents two generalizations of the notions of hitting and cover times to
weighted graphs. Indeed, the properties of random walks on symmetrically
weighted graphs provide interesting results on random walk based distributed
algorithms, such as local load balancing. Both of these generalization are
proposed to precisely represent the behaviour of these algorithms, and to take
into account what the weights represent. Then, we propose an algorithm to
compute the n^2 hitting times on a weighted graph of n vertices, which we
improve to obtain a O(n^3) complexity. This complexity is the lowest up to now.
This algorithm computes both of the generalizations that we propose for the
hitting times on a weighted graph. Finally, we provide the first algorithm to
compute the cover time (in both senses) of a graph. We improve it to achieve a
complexity of O(n^3 2^n). The algorithms that we present are all robust to a
topological change in a limited number of edges. This property allows us to use
them on dynamic graphs.; Comment: 18 pages

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## An Algorithm to Compute a Primary Decomposition of Modules in Polynomial Rings over the Integers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/08/2014
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We present an algorithm to compute the primary decomposition of a submodule
$\mathcal{N}$ of the free module $\Z[x_1, \ldots, x_n]^m$. For this purpose we
use algorithms for primary decomposition of ideals in the polynomial ring over
the integers. The idea is to compute first the minimal associated primes of
$\mathcal{N}$, i.e. the minimal associated primes of the ideal $\Ann(\Z[x_1,
\ldots, x_n]^m /\mathcal{N})$ in $\Z[x_1,\ldots,x_n]$ and then compute the
primary components using pseudo-primary decomposition and extraction, following
the ideas of Shimoyama-Yokoyama. The algorithms are implemented in {\sc
Singular}.; Comment: 10 pages

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## A Framework for Creating a Distributed Rendering Environment on the Compute Clusters

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/01/2014
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This paper discusses the deployment of existing render farm manager in a
typical compute cluster environment such as a university. Usually, both a
render farm and a compute cluster use different queue managers and assume total
control over the physical resources. But, taking out the physical resources
from an existing compute cluster in a university-like environment whose primary
use of the cluster is to run numerical simulations may not be possible. It can
potentially reduce the overall resource utilization in a situation where
compute tasks are more than rendering tasks. Moreover, it can increase the
system administration cost. In this paper, a framework has been proposed that
creates a dynamic distributed rendering environment on top of the compute
clusters using existing render farm managers without requiring the physical
separation of the resources.

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## Multistage Compute-and-Forward with Multilevel Lattice Codes Based on Product Constructions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/01/2014
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A novel construction of lattices is proposed. This construction can be
thought of as Construction A with codes that can be represented as the
Cartesian product of $L$ linear codes over
$\mathbb{F}_{p_1},\ldots,\mathbb{F}_{p_L}$, respectively; hence, is referred to
as the product construction. The existence of a sequence of such lattices that
are good for quantization and Poltyrev-good under multistage decoding is shown.
This family of lattices is then used to generate a sequence of nested lattice
codes which allows one to achieve the same computation rate of Nazer and
Gastpar for compute-and-forward under multistage decoding, which is referred to
as lattice-based multistage compute-and-forward.
Motivated by the proposed lattice codes, two families of signal
constellations are then proposed for the separation-based compute-and-forward
framework proposed by Tunali \textit{et al.} together with a multilevel
coding/multistage decoding scheme tailored specifically for these
constellations. This scheme is termed separation-based multistage
compute-and-forward and is shown having a complexity of the channel coding
dominated by the greatest common divisor of the constellation size (may not be
a prime number) instead of the constellation size itself.; Comment: 45 pages...

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## Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/04/2015
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The compute-and-forward framework permits each receiver in a Gaussian network
to directly decode a linear combination of the transmitted messages. The
resulting linear combinations can then be employed as an end-to-end
communication strategy for relaying, interference alignment, and other
applications. Recent efforts have demonstrated the advantages of employing
unequal powers at the transmitters and decoding more than one linear
combination at each receiver. However, neither of these techniques fit
naturally within the original formulation of compute-and-forward. This paper
proposes an expanded compute-and-forward framework that incorporates both of
these possibilities and permits an intuitive interpretation in terms of signal
levels. Within this framework, recent achievability and optimality results are
unified and generalized.; Comment: 47 pages, 10 figures, Submitted to IEEE Transactions on Information
Theory

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## Cooperative Compute-and-Forward

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/03/2012
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We examine the benefits of user cooperation under compute-and-forward. Much
like in network coding, receivers in a compute-and-forward network recover
finite-field linear combinations of transmitters' messages. Recovery is enabled
by linear codes: transmitters map messages to a linear codebook, and receivers
attempt to decode the incoming superposition of signals to an integer
combination of codewords. However, the achievable computation rates are low if
channel gains do not correspond to a suitable linear combination. In response
to this challenge, we propose a cooperative approach to compute-and-forward. We
devise a lattice-coding approach to block Markov encoding with which we
construct a decode-and-forward style computation strategy. Transmitters
broadcast lattice codewords, decode each other's messages, and then
cooperatively transmit resolution information to aid receivers in decoding the
integer combinations. Using our strategy, we show that cooperation offers a
significant improvement both in the achievable computation rate and in the
diversity-multiplexing tradeoff.; Comment: submitted to IEEE Transactions on Information Theory

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## Fast methods to compute the Riemann zeta function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The Riemann zeta function on the critical line can be computed using a
straightforward application of the Riemann-Siegel formula, Sch\"onhage's
method, or Heath-Brown's method. The complexities of these methods have
exponents 1/2, 3/8 (=0.375), and 1/3 respectively. In this paper, three new
fast and potentially practical methods to compute zeta are presented. One
method is very simple. Its complexity has exponent 2/5. A second method relies
on this author's algorithm to compute quadratic exponential sums. Its
complexity has exponent 1/3. The third method employs an algorithm, developed
in this paper, to compute cubic exponential sums. Its complexity has exponent
4/13 (approximately, 0.307).; Comment: Presentation simplified

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## Using boundary methods to compute the Casimir energy

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/03/2010
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We discuss new approaches to compute numerically the Casimir interaction
energy for waveguides of arbitrary section, based on the boundary methods
traditionally used to compute eigenvalues of the 2D Helmholtz equation. These
methods are combined with the Cauchy's theorem in order to perform the sum over
modes. As an illustration, we describe a point-matching technique to compute
the vacuum energy for waveguides containing media with different
permittivities. We present explicit numerical evaluations for perfect
conducting surfaces in the case of concentric corrugated cylinders and a
circular cylinder inside an elliptic one.; Comment: To be published in the Proceedings of QFEXT09, Norman, OK.

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## An Algorithm to Compute the Topological Euler Characteristic, the Chern-Schwartz-MacPherson Class and the Segre class of Subschemes of Some Smooth Complete Toric Varieties

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Let $X_{\Sigma}$ be a complete smooth toric variety of dimension $n$ defined
by a fan $\Sigma$ where all Cartier divisors in $\mathrm{Pic}(X_{\Sigma})$ are
nef and let $V$ be a subscheme of $X_{\Sigma}$. We show a new expression for
the Segre class $s(V,X_{\Sigma})$ in terms of the projective degrees of a
rational map associated to $V$. In the case where the number of primitive
collections of rays in the fan $\Sigma$ is equal to the number of generating
rays in $\Sigma(1)$ minus the dimension of $X_{\Sigma}$ we give an explicit
expression for the projective degrees which can be easily computed using a
computer algebra system. We apply this to give effective algorithms to compute
the Segre class $s(V,X_{\Sigma})$, the Chern-Schwartz-MacPherson class
$c_{SM}(V)$ and the Euler characteristic $\chi(V)$ of $V$. These algorithms
can, in particular, compute the Segre class, Chern-Schwartz-MacPherson class
and Euler characteristic of arbitrary subschemes of any product of projective
spaces $\mathbb{P}^{n_1} \times \cdots \times \mathbb{P}^{n_j}$ (over an
algebraically closed field of characteristic zero). Running time bounds for
several of the algorithms are given and the algorithms are tested on a variety
of examples. In all cases the algorithm to compute the Segre class is found to
offer significantly increased performance over other known algorithms. At
present we know of no other algorithms which compute Chern-Schwartz-MacPherson
classes and Euler characteristics in this setting.

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## Distributed Compute-and-Forward Based Relaying Strategies in Multi-User Multi-Relay Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper, we propose different practical distributed schemes to solve
the rank failure problem in the compute and forward (CMF)-based multi-user
multi-relay networks without central coordinator, in which the relays have no
prior information about each other. First, a new relaying strategy based on
CMF, named incremental compute-and-forward (ICMF), is proposed that performs
quite well in terms of the outage probability. We show that the distributed
ICMF scheme can even outperform the achievable rate of centralized optimal CMF
in strong enough inter relay links, with much less complexity. Then, as the
second scheme, amplify-forward and compute (AFC) is introduced in which the
equations are recovered in the destination rather than in the relays. Finally,
ICMF and AFC schemes are combined to present hybrid compute-amplify and forward
(HCAF) relaying scheme, which takes advantages of both ICMF, and AFC and
improves the performance of the ICMF considerably. We evaluate the performance
of the proposed strategies in terms of the outage probability and compare the
results with those of the conventional CMF strategy, the Decode and Forward
(DF) strategy, and also the centralized optimal CMF. The results indicate the
substantial superiority of the proposed schemes compared with the conventional
schemes...

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## Compute-and-Forward Two-Way Relaying

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In this paper, a new two-way relaying scheme based on compute-and-forward
(CMF) framework and relay selection strategies is proposed, which provides a
higher throughput than the conventional two-way relaying schemes. Two cases of
relays with or without feedback transmission capability are considered. An
upper bound on the computation rate of each relay is derived, and based on
that, a lower bound on the outage probability of the system is presented
assuming block Rayleigh fading channels. Numerical results show that while the
average sum rate of the system without feedback, named as Max
Compute-and-Forward (M-CMF), reaches the derived upper bound only in low SNRs,
that of the system with feedback, named as Aligned Compute-and-Forward (A-CMF)
reaches the bound in all SNRs. However, both schemes approach the derived lower
bound on the outage probability in all SNRs.; Comment: 27 pages, 9 figures, Accepted for IET Communications

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## High-Performance Compute Infrastructure in Astronomy: 2020 Is Only Months Away

Fonte: Astronomical Society of the Pacific
Publicador: Astronomical Society of the Pacific

Tipo: Book Section; PeerReviewed
Formato: application/pdf

Publicado em //2012
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By 2020, astronomy will be awash with as much as 60 PB of public data. Full scientific exploitation of such massive volumes of data will require high-performance computing on server farms co-located with the data. Development of this computing model will be a community-wide enterprise that has profound cultural and technical implications. Astronomers must be prepared to develop environment-agnostic applications that support parallel processing. The community must investigate the applicability and cost-benefit of emerging technologies such as cloud computing to astronomy, and must engage the Computer Science community to develop science-driven cyberinfrastructure such as workflow schedulers and optimizers. We report here the results of collaborations between a science center, IPAC, and a Computer Science research institute, ISI. These collaborations may be considered pathfinders in developing a high-performance compute infrastructure in astronomy. These collaborations investigated two exemplar large-scale science-driver workflow applications: 1) Calculation of an infrared atlas of the Galactic Plane at 18 different wavelengths by placing data from multiple surveys on a common plate scale and co-registering all the pixels; 2) Calculation of an atlas of periodicities present in the public Kepler data sets...

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